The sum of $6$ consecutive integers is $363$. What is the first number in this sequence?
Solution: Call the first number in the sequence $x$ The next integer in the sequence is $x + 1$ The sum of the $6$ consecutive integers is: $x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4)+ (x + 5) = 363$ $6x + 15= 363$ $6x = 348$ $x = 58$ Thus, the first number is $58$.